How would I go about doing this?
Doing what? You aren't giving much info here...
Normally, when I install the forum it is site.com/forum. I just want it to be site.com.
In your Control Panel on your hosting, Redirect "Site.com" --> "Site.com/forum"
So users typing either "Site.com" or "Site.com/forum" will both end up at "Site.com/forum."
is the forum already installed or this a new setup? if new, is there already content in the site's root folder?
Oor edit the settings in the ACP then move the files.
we should really find out if the OP has existing content in the site root so that those files do not get overwritten unexpectedly and break other parts of the site.